Subgroups — #15671315

Order 2944.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
5	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₁₆	C₄	1	4	yes	—
7	C₂×C₈×C₂₃	C₈	1	2	yes	—
8	C₂×C₈×C₂₃	C₈	1	2	yes	—
9	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
10	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂₃⋊C₁₆	—	2	4	no	—
12	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₂₃	—	2	2	no	—
16	C₈×C₂₃	C₁₆	1	4	yes	complemented
17	C₈×C₂₃	M₁₆	1	4	yes	—
18	#1312	—	23	1	no	maximal, Sylow
19	C₂²×C₂₃	C₄×C₈	1	1	yes	characteristic
20	C₄×C₂₃	#97	1	2	yes	—
21	C₄×C₂₃	C₂×C₁₆	1	2	yes	—
22	C₄×C₂₃	M₃₂	1	2	yes	—
23	C₄×C₁₆	—	23	2	no	—
24	C₈²	D₂₃	1	1	yes	characteristic
25	C₂×C₂₃	#322	1	1	yes	characteristic
26	C₂×C₂₃	C₄×C₁₆	1	1	yes	characteristic
27	C₂×C₂₃	#346	1	1	yes	characteristic
28	C₂×C₁₆	—	23	4	no	—
29	C₄×C₈	Dic₂₃	1	1	yes	characteristic
30	C₄×C₈	Dic₂₃	1	1	yes	characteristic
31	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
32	C₂₃	#1312	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	C₂₃⋊C₈	1	2	yes	—
34	C₂×C₈	C₂₃⋊C₈	1	2	yes	—
35	C₂×C₈	C₄×D₂₃	1	2	yes	—
36	C₄²	C₂×Dic₂₃	1	1	yes	characteristic
37	C₁₆	—	46	4	no	—
38	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
40	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	C₂₃⋊C₁₆	1	4	yes	complemented
43	C₈	#67262	1	4	yes	—
44	C₂²	C₄×C₂₃⋊C₈	1	1	yes	characteristic
45	C₄	C₂×C₂₃⋊C₁₆	1	2	yes	—
46	C₄	#10624994	1	2	yes	—
47	C₄	#10624997	1	2	yes	—
48	C₂	#13092138	1	1	yes	characteristic
49	C₂	C₄×C₂₃⋊C₁₆	1	1	yes	characteristic
50	C₂	#13092193	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₃
commutator	C₂×C₂₃	C₄×C₁₆
Fitting	C₈²×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₄×C₈
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	C₈²	D₂₃
hypocenter	C₂₃	#1312
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
16. C₈×C₂₃	C₁₆	semidirect
32. C₂₃	#1312	semidirect
42. C₈	C₂₃⋊C₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₂₃⋊C₁₆	2
C₈²×C₂₃	2
#1312	23